2=(-16t^2)+96t

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Solution for 2=(-16t^2)+96t equation: 


Simplifying
2 = (-16t2) + 96t

Reorder the terms:
2 = 96t + (-16t2)

Solving
2 = 96t + (-16t2)

Solving for variable 't'.

Reorder the terms:
2 + -96t + (16t2) = 96t + -96t + (-16t2) + (16t2)

Combine like terms: 96t + -96t = 0
2 + -96t + (16t2) = 0 + (-16t2) + (16t2)
2 + -96t + (16t2) = (-16t2) + (16t2)

Combine like terms: (-16t2) + (16t2) = 0
2 + -96t + (16t2) = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -48t + (8t2)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -48t + (8t2))' equal to zero and attempt to solve:

Simplifying
1 + -48t + (8t2) = 0

Solving
1 + -48t + (8t2) = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
0.125 + -6t + t2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -6t + -0.125 + t2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -6t + t2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -6t + t2 = 0 + -0.125
-6t + t2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-6t + t2 = -0.125

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = -0.125 + 9

Reorder the terms:
9 + -6t + t2 = -0.125 + 9

Combine like terms: -0.125 + 9 = 8.875
9 + -6t + t2 = 8.875

Factor a perfect square on the left side:
((t) + -3)((t) + -3) = 8.875

Calculate the square root of the right side: 2.979093822

Break this problem into two subproblems by setting 
((t) + -3) equal to 2.979093822 and -2.979093822.


Subproblem 1
(t) + -3 = 2.979093822

Simplifying
(t) + -3 = 2.979093822
t + -3 = 2.979093822

Reorder the terms:
-3 + t = 2.979093822

Solving
-3 + t = 2.979093822

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + t = 2.979093822 + 3

Combine like terms: -3 + 3 = 0
0 + t = 2.979093822 + 3
t = 2.979093822 + 3

Combine like terms: 2.979093822 + 3 = 5.979093822
t = 5.979093822

Simplifying
t = 5.979093822


Subproblem 2
(t) + -3 = -2.979093822

Simplifying
(t) + -3 = -2.979093822
t + -3 = -2.979093822

Reorder the terms:
-3 + t = -2.979093822

Solving
-3 + t = -2.979093822

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + t = -2.979093822 + 3

Combine like terms: -3 + 3 = 0
0 + t = -2.979093822 + 3
t = -2.979093822 + 3

Combine like terms: -2.979093822 + 3 = 0.020906178
t = 0.020906178

Simplifying
t = 0.020906178


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.979093822, 0.020906178}
Solution
t = {5.979093822, 0.020906178}

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